Wow, sounds like a mess. First of all, patient's don't get to decide how a visit should be billed, only the dr can dictate what service he performed. A medical visit with an EKG is certainly different than a routine checkup. And if a patient returns whether it is 3 days later, or the next day, or a month, it is a separate visit. Even if the first visit was billed as a checkup it wouldn't make the visit 3 days later not count.
The problem is that the provider is telling you to change it. Basically, since you were not present and you are the biller, you need to bill what the provider states was done. So if the provider is now stating that the visit should have been billed as an annual checkup then that is how you must bill it. But I would request that they send something over to you stating it was originally sent over incorrectly and this is the corrected way to be billed.
As far as insurance fraud, it depends on how it was recorded in the patient's chart. And they are not intentionally trying to get more money out of the insurance company, they are trying to appease the patients. (Not that that's how fraud is determined, but the insurance carriers are looking for providers intentionally cheating the system.)
Your in a tough place but all you can do is advise the provider as to how bill it out correctly, but in the end bill out the services that you are told were performed.
Good luck.
Michele